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The impact of faking on Cronbach’s alpha for dichotomous and ordered rating scores


  • Massimiliano Pastore


  • Luigi Lombardi



In many psychological inventories (i.e., personnel selection surveys and diagnostic tests) the collected samples often include fraudulent records. This confronts the researcher with the crucial problem of biases yielded by the usage of standard statistical models. In this paper we applied a recent probabilistic perturbation procedure, called sample generation by replacement (SGR)—(Lombardi and Pastore, Multivar. Behav. Res 47:519–546, 2012 ), to study the sensitivity of Cronbach’s alpha index to fake perturbations in dichotomous and ordered data, respectively. We used SGR to perform two distinct SGR simulation studies involving two sample size conditions, three item set sizes, and twenty levels of faking perturbations. Moreover, in the second SGR simulation study we also evaluated an additional factor, type of faking model, to study sample reliability under different modulations of graded faking (uniform faking, average faking, slight faking, and extreme faking). To simulate these more complex faking models we proposed a novel extension of the SGR perturbation procedure based on a discrete version of the generalized beta density distribution. We also applied the new procedure to real behavioral data on emotional instability. Copyright Springer Science+Business Media Dordrecht 2014

Suggested Citation

  • Massimiliano Pastore & Luigi Lombardi, 2014. "The impact of faking on Cronbach’s alpha for dichotomous and ordered rating scores," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(3), pages 1191-1211, May.
  • Handle: RePEc:spr:qualqt:v:48:y:2014:i:3:p:1191-1211
    DOI: 10.1007/s11135-013-9829-1

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    References listed on IDEAS

    1. P. Bentler & J. Woodward, 1980. "Inequalities among lower bounds to reliability: With applications to test construction and factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 249-267, June.
    2. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    3. Melvin Novick & Charles Lewis, 1967. "Coefficient alpha and the reliability of composite measurements," Psychometrika, Springer;The Psychometric Society, vol. 32(1), pages 1-13, March.
    4. Louis Guttman, 1945. "A basis for analyzing test-retest reliability," Psychometrika, Springer;The Psychometric Society, vol. 10(4), pages 255-282, December.
    5. Henry Kaiser & Kern Dickman, 1962. "Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix," Psychometrika, Springer;The Psychometric Society, vol. 27(2), pages 179-182, June.
    6. Adam Duhachek & Anne T. Coughlan & Dawn Iacobucci, 2005. "Results on the Standard Error of the Coefficient Alpha Index of Reliability," Marketing Science, INFORMS, vol. 24(2), pages 294-301, July.
    7. Ke-Hai Yuan & Peter Bentler, 2002. "On normal theory based inference for multilevel models with distributional violations," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 539-561, December.
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    Cited by:

    1. Luigi Lombardi & Massimiliano Pastore, 2016. "Robust evaluation of fit indices to fake-good perturbation of ordinal data," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(6), pages 2651-2675, November.


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